Power Transitional Reasoning Practice

Questions

1. 1.

   A construction site uses an electric hoist with an efficiency of 80% that draws a steady electrical power of 5.0 kW from the power supply. The hoist raises a pallet of building materials with a total mass of 400 kg vertically to a scaffolding platform located 15 m above the ground at a constant speed. Assuming negligible cable mass and taking the acceleration due to gravity as 10 m/s², how much time does this lifting operation take?

   • A) 12 s
   • B) 15 s
   • C) 19 s
   • D) 24 s
2. 2.

   An experimental hybrid vehicle of mass 1500 kg traveling at 24 m/s on a straight, level test track applies its regenerative braking system, slowing down smoothly to 8 m/s in a time interval of 4.0 s. During this deceleration, 75% of the vehicle's lost kinetic energy is converted into electrical energy and stored in the battery pack, while the rest is dissipated as thermal energy. What is the average electrical power delivered to the battery pack during this braking event?

   • A) 72 kW
   • B) 96 kW
   • C) 36 kW
   • D) 128 kW
3. 3.

   A competitive track cyclist rides along a level velodrome where aerodynamic drag is the dominant resistive force opposing motion. In this regime, the drag force magnitude is proportional to the square of the speed, expressed as $F_{\text{drag}} = kv^2$, where $k$ is a constant. The mechanical power required to maintain a constant speed against this force is given by $P = F_{\text{drag}}v$. If the cyclist increases their sustained mechanical power output by a factor of 8, by what factor does their steady cruising speed increase?

   • A) 1.4
   • B) 2.0
   • C) 2.8
   • D) 4.0
4. 4.

   An electric scooter and rider have a combined mass of 100 kg and ascend a straight road inclined at an angle where $\sin\theta = 0.10$ at a constant speed of 5.0 m/s. A combined rolling resistance and aerodynamic drag force of 60 N acts parallel to the road surface, opposing the motion. Taking the acceleration due to gravity as 10 m/s², what mechanical power must the motor deliver to sustain this motion?

   • A) 800 W
   • B) 500 W
   • C) 300 W
   • D) 200 W
5. 5.

   A light electric utility vehicle of mass 1200 kg accelerates uniformly from rest along a straight, horizontal test track, reaching a velocity of 20 m/s in a time interval of 8.0 s. Assuming that air resistance and mechanical friction are negligible, what is the instantaneous mechanical power delivered by the drive system at the instant $t = 6.0\text{ s}$?

   • A) 30 kW
   • B) 45 kW
   • C) 60 kW
   • D) 22.5 kW
6. 6.

   A commercial elevator cab with a mass of 1000 kg carries passengers having a combined mass of 200 kg. To reduce the energy demand on the drive system, a counterweight of mass 800 kg is suspended on the opposite side of the cable loop. If the drive motor raises the fully loaded cab vertically at a constant speed of 2.0 m/s, what is the minimum mechanical power that the motor must supply? (Take the acceleration due to gravity as $g = 10\text{ m/s}^2$ and neglect friction and cable mass.)

   • A) 4.0 kW
   • B) 8.0 kW
   • C) 16.0 kW
   • D) 24.0 kW
7. 7.

   A drainage pump continuously extracts water from a flooded underground chamber and discharges it through an outlet located 15 m above the intake level. The pump maintains a steady mass flow rate of 20 kg/s, and the water emerges from the outlet nozzle with a speed of 6 m/s. Neglecting internal dissipative losses in the pipe and taking the acceleration due to gravity as $10\text{ m/s}^2$, what is the minimum mechanical power that the pump delivers to the water?

   • A) 3.00 kW
   • B) 3.12 kW
   • C) 3.72 kW
   • D) 3.36 kW
8. 8.

   A prototype horizontal catapult system accelerates a 1200 kg rescue drone from rest to a takeoff speed of 30 m/s along a straight, frictionless launch rail in a time interval of 3.0 s. Neglecting air resistance, what is the average net power delivered to the drone during this launch?

   • A) 360 kW
   • B) 180 kW
   • C) 540 kW
   • D) 60 kW
9. 9.

   An electric vehicle travels at a steady speed of 25 m/s along a straight, horizontal highway where aerodynamic drag and friction exert a combined resistive force of 1600 N opposing its motion. If the vehicle's electric motor and drivetrain system operate with an overall efficiency of 80%, what is the electrical power drawn from the battery pack to sustain this cruising speed?

   • A) 50 kW
   • B) 40 kW
   • C) 32 kW
   • D) 20 kW
10. 10.

    A warehouse uses two electric hoists to elevate crates vertically at constant speed. Hoist X raises a 600 kg crate at a steady speed of 0.5 m/s, while Hoist Y lifts a 400 kg crate through a vertical height of 18 m in 20 s. Taking the acceleration due to gravity as 10 m/s², what is the ratio of the useful mechanical power delivered by Hoist X to that delivered by Hoist Y?

    • A) 6/5
    • B) 1
    • C) 5/6
    • D) 3/4

Answers and step-by-step solutions appear after you finish the test.